Scuba Diver Sees Bird: Refraction Problem Explained

[Irfan Nafi]

1. The problem statement, all variables, and given/known data
A scuba diver is underwater. She looks up and sees a bird flying in the sky. Compared to its actual distance, the bird appears to be...
1. Closer
2. At actual distance
3. Further

Homework Equations

n₁sin(θ₁)=n₂sin(θ₂)

The Attempt at a Solution

The light from the bird is bent towards the normal when it enters the water so it should appear to be closer than it actually is, assuming the same height of the apparent position of the bird. The actual answer is that it is at the actual distance, but that would mean that the apparent height of the bird would be greater than its actual height. How can this be explained and are there any flaws in my reasoning?

 

[Doc Al]

The light from the bird is bent towards the normal when it enters the water

Sounds good.

so it should appear to be closer than it actually is

How did you deduce this?

Imagine a few "rays" of light and trace their path. From what point do those rays appear to originate as seen from under the water?

 

[DoItForYourself]

I agree with your reasoning, but I think an appropriate figure would be very useful in this case.

 

[Irfan Nafi]

Here's a diagram :

 

[Doc Al]

Let me clarify my earlier suggestion: Draw several rays of light emanating from the bird and hitting the water. Then you can project the bent rays in the water to find their apparent source.

(The diagram you drew does not allow you to draw any conclusions. You need multiple rays. At least two! You have the correct direction for the ray, but not the correct apparent origin.)

 

[DoItForYourself]

Do you mean that the intersection point of the bent rays is the apparent source/origin?

 

[Irfan Nafi]

What's the apparent origin?

 

[Doc Al]

Do you mean that the intersection point of the bent rays is the apparent source/origin?

Yes.

What's the apparent origin?

The apparent location of the bird as seen from under the water. Locating that point is how you find the apparent distance of the bird.

 

[Irfan Nafi]

Sorry, the image is so large, but is this what you mean?

 

[haruspex]

Sorry, the image is so large, but is this what you mean?

That link is not working for me.

 

[DoItForYourself]

So, when the diver (eye) moves under the sea, the bird seems to be in the same apparent point.
It sounds rational.

 

[haruspex]

So, when the diver (eye) moves under the sea, the bird seems to be in the same apparent point.
It sounds rational.

Yes, but the diver does not need to move. Rays from a point source arrive at different parts of the lens and get focussed back to a point on the retina. The lens adjusts to compensate for the divergence between the rays. If the refraction alters the angle between the rays then the lens adjustment is different, leading to a different impression of distance.
Also, binocular vision has the same benefit as moving the head.

 

[Irfan Nafi]

I have the image attached.

 

[haruspex]

I have the image attached.

That does not give you the apparent height.
Use a single point on the object and trace two divergent rays from it. Either make the eye much wider to accommodate them or omit the eye.

 

[Irfan Nafi]

Oh, I got it. Thanks for the help.